Exact Analytic Spectrum of Relic Gravitational Waves in Accelerating Universe

An exact analytic calculation is presented for the spectrum of relic gravi-tational waves in the scenario of accelerating Universe Ω Λ + Ω m = 1. The spectrum formula contains explicitly the parameters of acceleration, inflation , reheating, and the (tensor/scalar) ratio, so that it can be employed for a variety of cosmological models. We find that the spectrum depends on the behavior of the present accelerating expansion. The amplitude of gravitational waves for the model Ω Λ = 0.65 is about ∼ 50% greater than that of the model Ω Λ = 0.7, an effect accessible to the designed sensitivities of LIGO and LISA. The spectrum sensitively depends on the inflationary models with a(τ) ∝ |τ | 1+β , and a larger β yields a flatter spectrum, producing more power. The current LIGO results rule out the inflationary models of β ≥ −1.8. The LIGO with its design sensitivity and the LISA will also be able to test the model of β = −1.9. We also examine the constraints on the spectral energy density of relic gravitational waves. Both the LIGO bound and the nucleosynthesis bound point out that the model β = −1.8 is ruled out, but the model β = −2.0 is still alive. The exact analytic results also confirm the approximate spectrum and the numerical one in our previous work.